The function with zeros -3,-1,0 and 6 is [tex]f(x)=x(x+1)(x+3)(x+6)[/tex]
Given that the function has zeros at -3, -1,0 and 6.
If a is a zero of a function f(x), then f(a)=0. Also (x-a) will be a factor of f(x).
Thus here, f(-3)=0, f(-1)=0,f(0)=0 and f(6)=0.
That is the function will have the factors (x+3), (x+1), x and (x-6).
Hence the function f(x) can be defined as the product of these factors.
Thus, the function with zeros -3, -1, 0 and 6 will be
[tex]f(x)=x(x+1)(x+3)(x+6)[/tex]
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